Homework.pdf

1. a. Table for wolf population growth:
Year: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Population: 20, 24, 28.8, 34.56, 41.472, 49.7664, 59.71968, 71.663616, 85.9963392, 103.19560704, 123.83472805
b. Explicit equation: P = 20(1.2)^t
c. Time to exceed 100 wolves: between 9 and 10 years
d. Graph: not provided

2. Time for trout to double: unknown, depends on initial population and growth factor
3. Equation for squirrel population: p = 500,000(1.6)^n
4. a. Growth factor: 2.9
b. Growth rate: 190%
5. a. Growth factor: 1.53
b. Growth rate: 53%
6. a. Tables for f(x) and g(x):
f(x) = 50(2.2)^x:
x: 0, 1, 2, 3, 4, 5, 6, 7, 8
y: 50, 110, 242, 533.2, 1172.64, 2579.488, 5673.6272, 12473.88064, 27463.337408
g(x) = 350(1.7)^x:
x: 0, 1, 2, 3, 4, 5, 6, 7, 8
y: 350, 595, 1008.5, 1714.65, 2915.005, 4962.5585, 8434.34925, 14338.192725, 24348.72722
b. Growth factors: 2.2, 1.7
c. Graphs will cross: yes
d. Estimated crossing point: unknown, depends on equations
7. a. Growth rate: 20%
b. Growth factor: 1.2
8. a. Value after 1 year: $315,000
b. Value after 2 years: $330,750
c. Value after 3 years: $347,837.50
d. Value after 30 years: $2,917,191.19
9. a. Explicit equation: A = 20,000(1.06)^x
b. Value after 5 years: $26,765.82
10. Growth factor: 3.5